Question

$20$ persons were invited to a party. In how many ways can they be seated in a round table such that two particular persons sit on either side of the host?

• A. $18!$
• B. $16!$
• C. $2\times 18!$
• D. none of these

Answer 1

The correct option is C $2\times 18!$

$20$ person $1$ host

Total number of people $=21$

$2$ people do not sit beside host

Concidering host and $2$ people one entity

$\Rightarrow$Number od people $=21-3+1$

$=19$ person

Number of ways of seating around the table

$=(19-1)!$

$=18!$ Ways

Two person can be seated in two ways

Total number of ways $=18!\times 2$ Ways